Alexa V. answered 04/25/19
Japanese Language and JLPT Prep from an Experienced Translator
Think of the first two as active actions with direct objects and the second two as passive actions without direct objects (I'm oversimplifying). I'm going to pick a few simpler verbs here to show you what I mean:
始める(他動詞): to start
始まる(自動詞): to start
The first verb is used in the case where the subject of the sentence is starting something. For example:
クラスを始めます。I am starting the class.
Notice that this uses を, the object particle.
The second verb is used in the case where something "is starting" (not necessarily on its own, but the subject of the sentence is not actively starting it). For example:
クラスが始まります。The class is starting.
Here, が is being used instead of を.
Likewise, 広める and 広げる involve the particle を as well as showing that someone is actively "widening" (enlarging, etc.) something. Meanwhile, 広まる and 広がる show that something is widening. I should note the particles are not always を and が, but they're pretty standard in this context.
Hope this helps! Let me know if you would like further explanation.